Question

3. The kinetic energy of an object of mass ‘m’ moving with a velocity of 5 ms-1 is 25 J. What will be its kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased three times.​

Answer 1

Answer :

• Kinetic energy of the body when the velocity is doubled is 100 J

• Kinetic energy of the body when the velocity is increased three times is 225 J

Explanation :

Given :

• Mass of the body, m = m

• Velocity of the body, v = 5 m/s

• Kinetic energy possessed by the body, KE = 25 J

To find :

• Kinetic energy of the body when the velocity is doubled , KE = ?
• Kinetic energy of the body when the velocity is increased three times, KE = ?

Knowledge required

By definition, Kinetic energy is the energy possessed by a body due it's state of motion or the energy possessed by a body of mass in some velocity.

So,

⠀⠀⠀⠀⠀⠀⠀⠀⠀K.E. = ½mv²

Where :

• K.E. = Kinetic energy possessed by the body
• m = Mass of the body
• v = Velocity of the body

Solution :

First let us find the mass of the body :

By using the Equation for Kinetic energy of a body and substituting the values in it, we get :

==> K.E. = ½mv²

==> 25 = ½ × m × 5²

==> 25 = 12.5 m

==> 25/12.5 = m

==> 2 = m

∴ Mass of the body = 2 kg

Now,

• Kinetic energy (K.E.) of the body when the velocity is doubled (i.e, Velocity = 2v) :

By using the equation for Kinetic energy possessed by a body and substituting the values in it, we get :

==> K.E. = ½mv²

==> K.E. = ½ × m × (2v)²

==> K.E. = ½ × 2 × (2 × 5)²

==> K.E. = ½ × 2 × 10²

==> K.E. = 10²

==> K.E. = 100

∴ Kinetic energy of the body = 100 J.

• Kinetic energy (K.E.) of the body when the velocity is increased three times (i.e, Velocity = 3v) :

By using the equation for Kinetic energy possessed by a body and substituting the values in it, we get :

==> K.E. = ½mv²

==> K.E. = ½ × m × (3v)²

==> K.E. = ½ × 2 × (3 × 5)²

==> K.E. = ½ × 2 × 15²

==> K.E. = 15²

==> K.E. = 225

∴ Kinetic energy of the body = 225 J.

Therefore,

• Kinetic energy of the body when the velocity is doubled is 100 J

• Kinetic energy of the body when the velocity is increased three times is 225 J

Answer 2

Answer:

Explanation:

the K.E(KINETIC ENERGY) of the object is 25 J.

So,

25=1/2*m*(5)2

Therefore,m=2 kg.

Now, when the velocity is doubled, velocity becomes=2*5=10 m/s(ms-1)

So,

K.E.=1/2*2*(10)2 =100 J.

Now,when the velocity is increased three times,the velocity will be=3*5=15m/s

Therefore,K.E.=1/2*2*(15)2 = 225 J.